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<div class="iris_headline">IRIS Toolbox Reference Manual</div>




<h2 id="modellang/min">min</h2>
<div class="headline">Define the loss function in a time-consistent optimal policy model</div>

<h4 id="syntax">Syntax</h4>
<pre><code>min(DISC) EXPRESSION;</code></pre>
<h4 id="syntax-for-exact-non-linear-simulations">Syntax for exact non-linear simulations</h4>
<pre><code>min#(DISC) EXPRESSION;</code></pre>
<h4 id="description">Description</h4>
<p>The loss function must be types as one of the transition equations. The <code>DISC</code> is a parameter or an expression defining the discount factor (applied to future dates), the <code>EXPRESSION</code> defines the loss fuction proper.</p>
<p>If you use the <code>min#(DISC)</code> syntax, all equations created by differentiating the lagrangian w.r.t. individual variables will be earmarked for exact non-linear simulations provided the respective derivative is nonzero.</p>
<h4 id="example">Example</h4>
<p>This is a simple model file with a Phillips curve and a quadratic loss function.</p>
<pre><code>!transition_variables
    x, pi

!transition_shocks
    u

!parameters
    alpha, beta, gamma

!transition_equations
    min(beta) pi^2 + lambda*x^2;
    pi = alpha*pi{-1} + (1-alpha)*pi{1} + gamma*y + u;</code></pre>

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<div class="copyright">IRIS Toolbox. Copyright &copy; 2007&#8212;2013 Jaromir Benes.</div>
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